Method for simulating deformation of rubber compound with filler particles

Abstract

A method for simulating deformation of rubber compound with filler particles, comprises the following steps: by the use of a scanning transmission electron microscope (STEM), data of STEM images of the rubber compound are acquired; based on the data of the STEM images, a dataset of a three-dimensional structure of the rubber compound is reconstructed; based on the dataset of the three-dimensional structure of the rubber compound, a finite element model of the rubber compound is generated so that the model comprises a domain of a rubber component divided into a finite number of elements, and domains of the filler particles each divided into a finite number of elements; on the elements of the rubber component, the stress dependence on strain rate of the rubber component is defined; and based on the finite element model, a simulation of deformation of the rubber compound is carried out.

1 . A method for simulating deformation of rubber compound including a rubber component and filler particles, comprising:
 a STEM image acquiring step in which, by the use of a scanning transmission electron microscope (STEM), data of STEM images of the rubber compound are acquired;   a three-dimensional structure reconstruction step in which, based on the data of the STEM images, a dataset of a three-dimensional structure of the rubber compound is reconstructed;   a finite element model generating step in which, based on the dataset of the three-dimensional structure of the rubber compound, a finite element model of the rubber compound is generated, so that the finite element model comprises a domain of the rubber component divided into a finite number of elements, and domains of the filler particles each divided into a finite number of elements;   a stress dependence defining step in which the stress dependence on strain rate of the rubber component is defined on the elements of the rubber component; and   a simulation step in which, based on the finite element model, a simulation of deformation of the rubber compound is carried out.   
     
     
         2 . The method according to  claim 1 , wherein
 in the STEM image acquiring step, the focal point of the scanning transmission electron microscope is set in a thickness center region of a specimen of the rubber compound.   
     
     
         3 . The method according to  claim 1 , wherein
 in the STEM image acquiring step, a specimen of the rubber compound is tilted with respect to the central axis of the scanning transmission electron microscope, and   the STEM images are took at different tilt angles of the specimen of the rubber compound while the focal point of the scanning transmission electron microscope is set in a thickness center region of the specimen of the rubber compound based on an apparent thickness measured along the direction of the electron beam axis across the specimen of the rubber compound.   
     
     
         4 . The method according to  claim 1 , wherein
 the thickness of the specimen of the rubber compound is 200 to 1500 nm.   
     
     
         5 . The method according to  claim 1 , wherein
 the thickness of the specimen of the rubber compound is 200 to 1500 nm, and   the distance between the specimen of the rubber compound and a detector for the transmission electrons of the scanning transmission electron microscope is 8 to 150 cm.   
     
     
         6 . The method according to  claim 2 , wherein
 the thickness of the specimen of the rubber compound is 200 to 1500 nm.   
     
     
         7 . The method according to  claim 2 , wherein
 the thickness of the specimen of the rubber compound is 200 to 1500 nm, and   the distance between the specimen of the rubber compound and a detector for the transmission electrons of the scanning transmission electron microscope is 8 to 150 cm.